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Vaccines exert a positive externality, reducing spread of disease from the consumer to others, providing a rationale for subsidies. We study how optimal subsidies vary with disease characteristics by integrating a standard epidemiological model into a vaccine market with rational economic agents. In the steady-state equilibrium for an endemic disease, across market structures ranging from competition to monopoly, the marginal externality and optimal subsidy are non-monotonic in disease infectiousness, peaking for diseases that spread quickly but not so quickly as to drive all consumers to become vaccinated. Motivated by the Covid-19 pandemic, we adapt the analysis to study a vaccine campaign introduced at a point in time against an emerging epidemic. While the nonmonotonic pattern of the optimal subsidy persists, new findings emerge. Universal vaccination with a perfectly effective vaccine becomes a viable firm strategy: the marginal consumer is still willing to pay since those infected before vaccine rollout remain a source of transmission. We derive a simple condition under which vaccination exhibits increasing social returns, providing an argument for concentrating a capacity-constrained campaign in few regions. We discuss a variety of extensions and calibrations of the results to vaccines and other mitigation measures targeting existing diseases.